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Published byPierce Murphy Modified over 6 years ago
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Objectives Solve quadratic equations by completing the square.
Write quadratic equations in vertex form.
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Vocabulary completing the square
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Read as “plus or minus square root of a.”
Reading Math
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Example 1: Solving Equations by Using the Square Root Property
Solve the equation. x2 = 121
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Example 1: Solving Equations by Using the Square Root Property
Solve the equation. x2 = 121 Is this the same as “What is the √(121)?”
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Example 2: Solving Equations by Using the Square Root Property
Solve the equation. x2 = 1296
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Example 3: Solving Equations by Using the Square Root Property
Solve the equation. 4x = 59
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Example 4 Solve the equation. 4x2 – 20 = 5
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If a quadratic expression of the form x2 + bx cannot model a square, you can add a term to form a perfect square trinomial. This is called completing the square.
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Example 5: Completing the Square
Complete the square for the expression. Write the resulting expression as a binomial squared. x2 – 14x +
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Example 6: Completing the Square
Complete the square for the expression. Write the resulting expression as a binomial squared. x2 + 9x +
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Example 7 Complete the square for the expression. Write the resulting expression as a binomial squared. x2 + 4x +
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Example 8 Complete the square for the expression. Write the resulting expression as a binomial squared. x2 – 4x +
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Example 9 Complete the square for the expression. Write the resulting expression as a binomial squared. x2 + 3x +
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You can complete the square to solve quadratic equations.
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Example 11: Solving Equations
Solve the equation. x2 + 12x + 6 = 0
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Example 12 Solve the equation. x2 + 8x - 33 = 0
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Example 13: Solving a Quadratic Equation by Completing the Square
Solve the equation by completing the square. x2 = 12x – 20
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Example 14: Solving a Quadratic Equation by Completing the Square
Solve the equation by completing the square. 18x + 3x2 = 45
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Example 15 Solve the equation by completing the square. x2 – 2 = 9x
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Example 16 Solve the equation by completing the square. 3x2 – 24x = 27
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